School Science Lessons
Topic 6 Measurement, SI units, SYSTEME INTERNATIONAL D'UNITES
Updated 2009-10-11
Please send comments to: J.Elfick@uq.edu.au
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Table of contents
3.1.0 Counting, digital system, decimal system, binary system.
6.2.0 Different measurements
6.3.0 International system of units (SI)
SI units, SYSTEME INTERNATIONAL D'UNITES (French)
6.3.1 SI, The 7 base units
6.3.3.0 SI derived units
6.3.3.1 Other derived units based on SI
6.3.3.5 Units used with SI units
6.3.01, Angle
6.3.02 Pressure
12.1.04 Atmospheric pressure
6.3.03 Velocity, (speed)
6.3.04 Force, (weight)
6.3.05 Area (shape)
6.3.06 Volume
6.3.5 SI prefixes
6.3.6 SI, CGS and FPS conversion, metric conversion
6.3.1.1 Length, metre
6.3.1.2 Mass, kilogram
6.3.1.3 Time, second
6.3.1.4 Electric current, ampere
6.3.1.5 Temperature, Fahrenheit scale, Celsius scale, Kelvin scale
5.1.0 Mole, amount of substance
5.1.1 Prepare molar solutions
6.3.1.7 Luminous intensity, candela, cp
3.3.1.0 Accuracy and error
3.7.0 Ratio and proportion, concentration, degrees proof
3.6.0 Estimating
3.9.0.0 Non-SI units
3.5.4 Miscellaneous measures
2.0.0 Mathematics
6.4.0 Errors, theory of errors, addition of uncertainties
6.3.3.5 Units used with SI units: Area, Mass, Pressure, Volume
6.3.05 Area (shape)
3.4.0 Area, square metre (m2) hectare
6.6.3 Surface / volume ratio of soil particles
1.22 Compare different shapes (Primary)
1.23 Make new shapes (Primary)
1.24 Seeds and seed pods (Primary)
1.44 Area game (Primary)
4.17 Shapes game (Primary)
6.3.06 Volume (vol.) cubic metre (m3)
3.5.0 Volume (vol.) cubic metre (m3)
6.6.3 Surface / volume ratio of soil particles
3.5.1 Spoon volume
3.5.2 British liquid measures, imperial measures (fl. oz. = imperial fluid ounce)
3.5.3 American liquid measures, US measures, United States weights and measures, volume (liquid)
3.5.4 Miscellaneous measures
1.25 Pouring water game (Primary)
3.18 Volume of our fist (Primary)
3.23 Volume of a liquid (Primary)
2.1.6 Volume of liquid
3.18 Volume of our fist (Primary)
3.23 Volume of a liquid (Primary)
4.20 Measure chest expansion (Primary)
6.16 Measure air breathed out (Primary)
3.7.0 Ratio and proportion, concentration, degrees proof
6.6.3 Surface / volume ratio of soil particles
Surface / volume ratios of small block and large block. Surface / volume ratio of small cell and large cell.
Concentration. Dilution. "Degrees proof"
Relative size of electron, atom, molecule, cell, man and woman, earth.
3.7.1 Concentration
3.7.2 Degrees proof, proof spirit
2.0.2 Golden mean
3.9.0.0 Non-SI units
3.3.3.0 United States lineal weights and measures
3.3.4.0 United States surface (land) weights and measures
3.5.1 Spoon volume
3.5.2 British liquid measures, imperial measures (fl. oz. = imperial fluid ounce)
3.5.3 American liquid measures, US measures, United States weights and measures, volume to liquid
3.5.4 Miscellaneous measures
3.5.5 Nautical measures
3.9.0 CGS units (centimetre, gram, second)
3.10.0 The m.k.s. units
3.11.0 Imperial units used in land surveying (1 hectare = 10 000 m2, 1 km = 1 000 m)
3.12.0 SI, CGS and FPS conversion, metric conversion
3.13.0 Energy conversion KJ, MJ, KWh, therm, BTU, calorie, horsepower
3.13.1 Einstein was right, e = mc2
3.13.1.1 Quark
6.3.3.14 Viscosity, poise
2.0.0 Mathematics
2.22 Copy with a rubber band
2.0.3 Greek alphabet, phonetic alphabet
2.0.5 Conic sections, parabola, ellipse, hyperbola
2.0.6 Parabola equation
2.0.7 Change scale of a map
2.0.8 Mathematics for science teachers
6.13.0 Roman numerals
3.3.5.0 Graph measurements
3.3.6.0 Graph the speed of two cars
3.3.7.0 Table of numerals adding vertically or horizontally or diagonally to 33
3.2.2 Rank scaling tables
6.3.3.0 SI derived units: Acceleration, Angle (plane angle), Density, Electric capacitance, Electric charge, Electric potential difference, Electric resistance, Energy (work), Force, Frequency, Momentum, Power, Pressure (stress), Radioactivity, Velocity (speed), Viscosity
6.3.01, Angle
6.3.3.2 Angle, degree, arc minute, arc second, radian
2.0.1 Right-angled triangle
3.3.3.3 Line of vision
6.3.02, Pressure
6.18 Measure air pressure (Primary)
6.3.03, Velocity (speed)
3.13.1 Einstein was right, e = mc2
5.23 Wind speed and direction (Primary)
6.3.04, Force
2.16 Compare our weights (Primary)
2.23 See-saw balance (Primary)
2.24 Steelyard balance (Primary)
2.25 Make a ruler balance (Primary)
2.26 Balance bottle tops (Primary)
2.27 Nail balance (Primary)
2.28 Beam balance (Primary)
2.29 Drinking straw balance (Primary)
4.21 Measure our weight (Primary)
6.11 Forces on coins on a slope (Primary)
3.17 Make a plumb bob (Primary)
3.19 Single pan balance (Primary)
6.10 Pull with pulleys (Primary)
6.3.1.1 Length, metre
2.0.9 Handspans, trundle wheel
3.3.1.0 One Angstrom unit
3.3.2.0 One Astronomical unit
3.5.5 Nautical measures
1.14 Mark our height (Primary)
1.19 Length game (Primary)
1.20 Pace distances (Primary)
2.14 Measure in hand spans (Primary)
2.15 Measure with your body (Primary)
3.21 Trundle wheel (Primary)
3.15 Record our heights (Primary)
4.14 Length game (Primary)
4.15 Pace distances (Primary)
5.22 Rain gauge (Primary)
4.18 Diameter of a thread (Primary)
6.3.1.2 Mass, kilogram
3.2.1 Avoirdupois weight
3.2.2 Carat
3.2.3 Troy weight
3.2.4 Apothecaries' weight
6.12.0 Weights of one matchbox full of fertilizer
6.3.1.3 Time, second
3.22 Throw up and fall down (Primary)
4.24 Speed of reaction (Primary)
6.22 Pendulum tells the time (Primary)
6.3.1.5 Temperature, Fahrenheit scale, Celsius scale, Kelvin scale
6.3.1.5.1 Triple point and ice point temperatures of water
6.14.0 Oven temperatures
3.24 Air temperature (Primary)
6.17 Measure relative humidity (Primary)
6.3.3.5 Units used with SI units: Area, Mass, Pressure, Volume
Area
3.4.0 Area, square metre (m2) hectare
1.22 Compare different shapes (Primary)
1.23 Make new shapes (Primary)
1.24 Seeds and seed pods (Primary)
1.25 Pouring water game (Primary)
1.44 Area game (Primary)
4.17 Shapes game (Primary)
Volume (vol.) cubic metre (m3)
3.5.1 Spoon volume
3.5.2 British liquid measures, imperial measures (fl. oz. = imperial fluid ounce)
3.5.3 American liquid measures, US measures, United States weights and measures, volume (liquid)
3.5.4 Miscellaneous measures
3.18 Volume of our fist (Primary)
3.23 Volume of a liquid (Primary)
2.1.6 Volume of liquid
3.5.0 Volume (vol.) cubic metre (m3)
3.18 Volume of our fist (Primary)
3.19 Single pan balance (Primary)
3.23 Volume of a liquid (Primary)
4.20 Measure chest expansion (Primary)
6.16 Measure air breathed out (Primary)
3.3.1.0 Accuracy and error
3.3.1.1 Significant digits and standard form, scientific notation
3.3.2.1 Order of magnitude (nearest power of ten, a factor or factors of ten)
3.3.3.0 Factors that affect readings, obtain data from the equipment
3.3.3.1 Relative positions between measured object and equipment +
3.3.3.2 Reaction time of the equipment
3.3.3.3 Line of vision
3.3.4.1 Record measurements in tables
3.3.5.0 Graph measurements
3.3.6.0 Graph the speed of two cars
3.3.7.0 Table of numerals adding vertically or horizontally or diagonally to 33
3.2.2 Rank scaling tables
3.7.0 Ratio and proportion, concentration, degrees proof
3.7.1 Concentration
3.7.2 Degrees proof, proof spirit
3.2.1 Avoirdupois weight, English and United States weights and measures
1 avoirdupois weight pound (lb) = 16 ounces (oz). All chemicals were sold by avoirdupois weight. (Latin: pondus (weight), 12 ounces of pure silver, 240 pennies, so cash to the value of 20 shillings sterling, symbol lb (Latin: libra (cash pound))
pound
.
 ounce
.
 drachm,
dram
 grain,
(Troy)
 g
.
1
 16
 256
 7 000
 453.60
.
 1
 16
 437.5
 28.35
.
 .
 1
 27.34
 1.771 845
A fluid dram is 1 ⁄ 8 of a fluid ounce, i.e. 3.696 mL USA and 3.551 mL UK. In Scotland, a dram is a small volume of Scotch whisky.
3.2.2 Carat
For precious stones, 1 carat is about 1 / 142 of an ounce. For gold, a carat is a ratio of 1/24. Purity of gold is measured in carats. 24 carat gold is pure gold. 22 carat gold is 22 parts pure gold and 2 parts copper or other metal alloy. 14 carat gold is 14 parts pure gold and 14 parts copper or other metal.
The official mark stamped on gold and silver objects after being assayed is the hall mark (from Goldsmith's Hall, London). For gold, the standard mark is a crown in England for 22 and 18 carat gold followed by the number of carats in figures. Lower standards of gold have the number of carats in figures without the crown.
3.2.3 Troy weight
Gold is still sold in troy ounces, as were precious metals. 1 troy weight pound, lb = 12 troy ounces. 1 grain = 6.479 X 10-5 kg.
pound
 ounce
 pennyweight, dwt grain
 g
1
 12
 240
 5 760
 373.24
.
 1
 20
 480
 31.10
.
 .
 1
 24
 1.56
3.2.4 Apothecaries' weight, English and United States weights and measures
Apothecaries' measures were formerly used in pharmacy and were usually adopted in formulas. 1 fluid ounce = 8 drachms = 489 minums. The pound, ounce and grain are the same as in Troy weight.
In UK, the fluid drachm, fluidrachm = 3.55 mL.
pound
 ounce
 drachm
 scruple
 grain
 g
1
 12
 96
 288
 5 760
 373.24
.
 1
 8
 24
 480
 31 103
.
 .
 1
 3
 60
 3 888
.
 .
 .
 1
 20
 1.30
.
 .
 .
 .
 1
 0.06
3.3.0 Length (l) the kilometre (km) metre (metre)
Callipers, Vernier callipers, Vernier scale, callipers are for measuring internal and external diameters.
Gauge, feeler gauges, micrometer screw gauges
Find the thickness of one sheet of paper in a pile
Rule, measuring timber for carpentry, tape measure, dressmaking measurements: circumference of the chest / waist / hips, trundle wheels to measure the length of a crooked path
1 kilometre, 1 km = 1 000 metres
1 decimetre, 1 dm = 0.1 metre
1 centimetre, 1 cm = 0.01 metre
1 millimetre, 1 mm = 0.001 metre
1 micrometre, 1 mu m = 1 X 10-6 metre, one millionth of a metre, micron
1 nanometre, 1 nm = 10-9 metre, one billionth of a metre
1 picometre, 1 pm = 10-12 metre
3.3.1.0 One Angstrom unit, A = 10-10 metre, previously used as unit of measurement of wavelength but nowadays use nanometre. (Note: 1 nm = nanometre = 10 Angstrom units = 10-9 m.)
3.3.2.0 One Astronomical unit, AU = the mean distance between the Earth and the sun, about 149 598 000 km (92 956 000 miles). It is used as a convenient way to measure distance in the solar system.
3.3.1.1 Significant figures and standard form, scientific notation
1. Significant figures are all the figures that can be read with meaning from an instrument. Significant figures of a number are the digits that contribute to its value. For measurement, the significant figures are those you know with certainty plus the digit that is uncertain. A "2 tonne truck" could weigh between 1.5 and 2.5 tonnes. A reading of 25 cm could have a value between 24.5 and 25.5 cm. So you say that the last digit is uncertain. You count zeros between integers and zeros to the right of the decimal point following non-zero integers. You do not count other zeros. The following examples each have four significant figures:
0.01 234
0.1 023
0.1 230
In the last case you are saying that the reading is closer to 0.1 230 than 0.1 229 or 0.1 231. So be careful about zeros, especially the last zero.
2. If rounding off to 3 significant figures:
4.657 becomes 4.66 because 7 > 5.
4.655 becomes 4.66 because last digit is 5 and digit behind it is odd.
4.645 becomes 4.64 because last digit is 5 and digit behind it is even.
4.654 becomes 4.64 because 4 < 5.
3. When adding or subtracting, all numbers must have the same number of digits after the decimal point. This is equal to the least number of digits after the decimal point of any number in the addition or subtraction.
19.43 + 6.456 + 101.9 becomes 19.4 + 6.5 + 101.9 =127.8
4. When multiplying or dividing numbers, the answer can have only as many significant figures as the number with the least number of significant figures. 17.9 X 4.3 = 76.97 Answer = 77 (4.3 has only 2 significant figures)
5. Standard form or scientific notation expresses a number as a product of a number between 1 and 10 and a power of 10. It is a convenient way to express large and small numbers for easy comparison and it can show the number of significant figures. So you can write 18 000 as 1.8 X 104 (2 significant figures, i.e. the value is between 1.7 and 1.9 X 104), or 1.80 X 104 (3 significant figures, i.e. the value is between 1.79 and 1.81 X 104). Express decimal fractions in standard form: 0.1 = 1 X 10-1, 0.019 = 1.9 X 10-2
Standard form (scientific notation), e.g. 8.04 X 102, shows the significant figures expressed unambiguously. The coefficient, 8.04, must be greater than or equal to 1 and less than 10. The base number 10 is written in exponent form, so in 8.04 X 102, the number 2 is the exponent or power of ten.
Express decimal fractions in standard form, e.g.
0.1 = 1 X 10-1
0.2 = 1 X 10-2
0.019 = 1.9 X 10-2
0.00 087 = 8.7 X 10-4
3.3.2.1 Order of magnitude (nearest power of ten, a factor or factors of ten) +
Order of magnitude is a value expressed to the nearest power of ten. Sometimes you are interested in knowing the approximate rather than the precise values, so you just use the nearest power of ten, e.g. speed of light: 3.0 X 108 ms-1 = (approx.) 108 ms-1, the radius of the Earth: 6.38 X 106 m = (approx.) 10 X 106 m= 107 m, the radius of the Moon = 3.8 X 108 = (approx.) 109 m (3.8 is closer to 100 (1) than to 101 (10), 3.8 is greater than 10 ½ = 3.14).
3.3.3.1 Relative positions between measured object and equipment +
When you read on a scale with a measured object directly touching with the equipment, you must be careful as their relative position will probably affect precision of your readings. For example, if you measure temperature of liquid by a thermometer, you must immerse completely the measuring bulb in the liquid as you take readings.
3.3.3.2 Reaction time of the equipment
Some equipment reacts to measured quantities very quickly, such as meters for measuring electricity. However, some equipment needs a certain reacting time, such as a mercury thermometer. So you must take readings after the equipment stabilizes. Even with equipment that reacts quickly you need to pay attention to such problems, e.g. when measuring electric potential, be certain that the pointer no longer moves before you read from the scale.
3.3.3.3 Line of vision
The angle between your line of vision and the object referred to can cause errors. Your eye should be at right angles to the scale and directly opposite the part of the scale you are reading. Reading a scale from the left side or the right side or above or below are all wrong because they result in parallax error.
3.3.4.1 Record measurements in tables
Set up a table vertically if there is a possibility of additional requiring some extra space. Include a title and table number on the top of a table to state what data the table contains. The first column should contain data for the independent variable rather than the dependent variable. The weight is the independent variable because you decide its values, usually before doing the experiment. The increase in length of spring is the dependent variable because it depends on the weight added. Express all data in standard form.
Increase in length of spring. (Original length = 28.0 cm)
Weight
(N)		 Length of spring
(cm)		 Increase in length
(cm)
0.49 (0.5 kg) 32.8 4.8
0.98 (1 kg) 36.3 8.3
1.47 (1.5 kg) 39.4 11.4
1.96 (2.0 kg) 41.9 13.9
3.3.3.0 United States lineal weights and measures
foot (singular) feet (plural) (mile: Latin: mille 1 000, 1 000 paces, about 1 680 yards)
mile
 furlong
 rod
 yard
 foot
 inch
1
 8
 320
 1 760
 5 280
 63 360
.
 1
 40
 220
 660
 7 920
.
 .
 1
 5.5
 16.5
 198
.
 .
 .
 1
 3
 36
.
 .
 .
 .
 1
 12
3.3.4.0 United States surface (land) weights and measures
1 square foot = 144 square inches
1 square yard = 9 square feet
1 square rod = 30.25 square yards
1 square rood = 40 square rods
1 acre = 4 square rods
1 square mile = 640 acres = 2 560 roods = 102 400 rods = 3 097 600 square yards = 27 878.400 square feet
acre
 rood
 rod
 yard
 foot
1
 4
 160
 4 840
 43 560
.
 1
 40
 1 210
 10 890
.
 .
 1
 30.25
 272.25
.
 .
 .
 1
 9
3.3.5.0 Graph measurements
Area "under" a curve
Interpreting graphs. Linear graphs. Gradient (slope of a graph). Intercepts on a graph.
The graph of Y varies directly with X, e.g. Weight on spring.
The graph of Y varies inversely with X, e.g. PV of gas.
The graph of Y varies directly with X2, e.g. acceleration
A graph is a drawing that shows the relationship between variables.
Terminology: Axes of a graph, co-ordinates of a position on a graph, independent variable, dependent variable, line of best fit, area "under" a curve, interpreting graphs, linear graphs, gradient (slope of a graph), intercepts on a graph.
The graph of Y varies directly with X, e.g. weight on spring.
The graph of Y varies inversely with X, e.g. PV of gas.
The graph of Y varies directly with X2, e.g. acceleration.
3.3.5.1 Select scales
Select the scale of the axes to make the shape of the graph display the relation between data. The starting a point of the co-ordinate axis does not have to begin with zero and the scales of the two axes need not be the same. The variable you set up is the independent variable and is placed on the horizontal axis, the x axis. The variable that results from the independent variable is the dependent variable and is placed on the vertical axis, the y axis. If you investigate the cooling of a bucket of water, time is the independent variable and temperature of the water is the dependent variable. When you say "Graph speed against time" or "Draw a velocity time graph", then "time" is the independent variable because you have mentioned it after the dependent variable "speed". You show the position of any plotted point as (XY).
3.3.5.2 Plot points and draw by hand
See diagram 2.0.4.1: Drawing a graph
When plotting points in the co-ordinate system by hand the symbols may be small dots surrounded by a circle or a thin cross shape. In the diagram, the computer using "brush" from the Windows XP Paint program has generated the symbols. When you have two graphs in one co-ordinate system, different symbols should express the points in different graphs. Do not graph if less than 6 points. Draw the graph by using the inner drawing method so that your wrist that is a centre to turn around in forming a smooth graph. Check the points that are far from the graph because measuring them again may be necessary. A dotted line should express a graph that you have deduced to distinguish from the graph obtained from experiment.
3.3.6.0 Graph the speed of two cars
See diagram 2.0.4.2: Speed of two cars
Suppose you mark a straight road every 10 metres and can use a stopwatch to record when a car reaches each mark. The following table shows your data for 2 cars, car A and car B. In the graph the points for Car A are almost in a straight line. You can say that the line of best fit is a straight line. However, the graph line does not go exactly through each point because some experimental error can occur when reading the stopwatch, recording the data and plotting the graph. However, if you assume that the graph line is properly straight then you can say that each quantity is proportional to the other, distance = speed (velocity) X time, d = vt. Car A was moving with constant speed 4.2 m / s. Estimate how far Car A had moved after 8 seconds, by interpolation = 33 m. See the P on the graph. Estimate how far Car A had moved after 8 seconds, by calculation, d = vt, d =4.2v X 8 t = 33.6 m.
Car A
Distance
(m)		 Elapsed time
(seconds)		 Speed
(m / s)
0 0 0
10 2.3 4.3
20 4.9 4.1
30 7.1 4.2
40 9.7 4.1
50 12.0 4.2
.
 .
 Average speed = 4.18 = 4.2
In the graph the points for Car B are not in a straight line. The line of best fit is a curve so the speed is constantly changing. The graph shows the method of calculating the instantaneous speed at two distances 15 m and 35 metres. Draw a tangent to the point on the graph corresponding to the distance. Construct a right angle triangle with the tangent as hypotenuse then read the corresponding values for for distance and time from the two sides of the triangle then calculate the speed, v = d / t. At 15 m, the instantaneous speed was s / t, 10 d / 3.2 t = 3.125 m / sec. = 3.2 m / sec. At 35 m, the instantaneous speed was s / t, 10 d / 7.8 t = 6.25 = 6.2 m / sec.
Car B
Distance
(m)		 Elapsed time
(seconds)		 Instantaneous speed
(m / sec.)
0 0 .
10 4.0 (15 m, 3.2 m / sec
20 7.0 .
30 8.9 (35 m. 6.2 m / sec)
40 10.5 .
50 12.0 .
3.3.7.0 Table of numerals adding vertically or horizontally or diagonally to 33
1
 14
 14
 4
11
 7
 6
 9
8
 10
 10
 5
13
 2
 3
 15
3.4.0 Area, square metre (m2) hectare
Land: 100 metres (m) x 100 metres (m) = 10 000 square metres (m2) = (104 m2) = 1 hectare (ha) = 2.471 acre = 107 639 ft2
Imperial units used in land surveying (1 hectare = 10 000 m2, 1 km = 1 000 m)
Area of cloth for a dress, area of a bolt of cloth, floor cover, area of a fitted carpet.
Irregular shape area, use of graph paper.
Regular shape area, square, rectangle, circle
Area of the top of a matchbox: 20 cm2
3.5.0 Volume (vol.) cubic metre (m3)
See diagram 2.1.6: Liquid volume
Volume in a measuring cylinder, meniscus
Volume of a bucket, fish tin, coconut, cups, a tablespoon, a teaspoon, of cooking oil to be used for food, of agricultural chemical to be used on a farm
Volume of water used at home or school, reading a water meter
Volume of petrol (gasoline) used by a motor vehicle
Volume of irregular shapes, volume of small quantity of sand or glass beads.
Displaced volume, overflow vessels
Volume of regular shapes, a cube, a block, cylinder, sphere, cone
Volume of gas used at home or school, reading a gas meter
Volume, solid: 1 centimetre (cm) x 1 centimetre (cm) x 1 centimetre (cm) = 1 cubic centimetre (1 cc, 1 cm3) = 1 millilitre, 1 mL
1 cubic decimetre, 1dm3 = 1 litre , 1 L = 1000 mL = 1000 cm3 = 1000 cc
Volume, liquid: 1 000 millilitres = 1 litre (L)
Mole
1 mole, 1 M = 1 mol. dm-1 = 1 mole per cubic decimetre = 1 mole per litre = 1 mol. L-1
3.5.1 Spoon volume
1 teaspoon (the smallest spoon) = 4.5 to 5 mL (0.2 fl oz) (1 fluid dram)
1 dessertspoon (the spoon you eat with) = 10 mL
1 tablespoon (tblspn) (spoon to serve with, the biggest spoon): 15 to 20 mL (0.5 fl oz)
1 teacup (cup to use with a saucer): 250 mL
1 matchbox volume: 25 mL
3.5.2 British liquid measures, imperial measures (fl. oz. = imperial fluid ounce)
These measures were usually adopted in formulas.
1 fluid ounce = 28.42 mL (0.96 US oz)
1 imperial pint = 568.3 mL (20 fl oz)
1 quart = 1140 mL (40 fl oz) (38.5 US oz)
1 imperial gill = 0.132 L (5 fl oz)
1 imperial gallon = 4.54 609 litres, 4.55 L
1 fluid drachm = 60 minims
1 fluid ounce = 8 fluid drachms
1 pint = 20 fluid ounces
1 gallon = 8 pints
3.5.3 American liquid measures, US measures, United States weights and measures, volume to liquid
1 liquid US pint = 473.1 mL (473.179 cc) (16 fl oz)
1 dry US pint = 550.6 mL (19 fl oz)
1 US fluid ounce = 29.56 mL (29.574 cc)
1 US gill = 0.118 L
1 US gallon = 3.79 L (3 785.435 cc)
1 pint = 4 gills
1 quart = 2 pints
1 gallon = 4 quarts (231 cubic inches)
3.5.4 Miscellaneous measures
1 wine glass to 1/4 cup
1 jigger = 1.5 fl oz
1 peck = 2 dry gallons
1 pinch or dash = what you pick up between your thumb and first two fingers
½ pinch = to what you can pick up between your thumb and one finger
1 salt spoon = 1/4 teaspoon
1 penny weight = 1/20 fl. oz
1 drachma = 1/8 oz
1 cup, cupful = 284 mL
To measure 1 / 4 cup of butter, half fill a cup witrh water and slowly introduce add a slab of butter until the water rises to the 3 / 4 level.
1 teacup (the cup you use with a saucer) = 200 mL
1 matchbox volume = 25 mL, Area of the top of a matchbox = 20 cm2
1 barrel (bbl) of crude oil = 42 US gallons, = 34.97 Imperial gallons (about 159.1 litres)
Foolscap printing paper = 13.5 X 17 inches
Foolscap writing paper = 13.25 X 16.5 inches
1 kati, caddy = 1 lb, 5 oz, 2 dr, weight still used in Hong Kong and Malaysia
1 cubit = 18 inches (English) 17.5 inches (Roman) 21 inches (Egyptian) traditionally measured from the tip of the elbow to the tip of the longest finger
1 hundredweight, 1 C-wt., 1 / 20 ton, long hundredweight (50.8 kg)
1 metric hundredweight 50 kg
1 US hundredweight 100 lb, short hundredweight (45.3 kg)
1 ell = 45.5 cm (English), 37 cm (Scotch), 54 cm (French), cloth measure from elbow to finger tips
1 hair breadth = 1 inch / 48
1 magnum = 2 English wine bottles (2 "reputed" quarts)
1 jeroboam = 4 English wine bottles = 4 X 262/3 fluid ounces
1 rehoboam = 6 English wine bottles
1 jerrican = 41/2 gallons (used for military fuel)
1 journey-weight of gold = 15 pounds troy (701 sovereigns)
1 nail = formerly a weight of 8 pounds or a length of 2.25 inches
1 barrel (beer cask) = 32 imperial gallons
1 barrel (petroleum) = 35 imperial gallons (about 159 L)
Human body temperature 37oC (Celsius)
3.5.5 Nautical measures
Ship's cable was measured in shackles, 1 shackle = 12.5 fathoms
8 shackles, 100 fathoms, = 1 nautical mile / 10
The international nautical mile is 1 852 m. The UK nautical mile is 1 853.18 m (6 080 ft) its value in latitude 48o. A speed of one nautical mile per hour is one knot.
3.6.0 Estimating
See 6.21: Estimating experiments (Primary)
Estimating of parameters, prediction, size perception, relative size
Estimating height of people, tree, a house, bridge, mountain
Estimating distance from the roadside, of the car ahead
3.7.1 Concentration
See 7.7.0: Solutions, solubility, molar solution, solubility equilibrium, solubility product, solubility rules
Concentration is the quantity of dissolved substance to quantity of solvent.
Dilution is the volume of solvent in which a measured amount of solute is dissolved.
Different ways of expressing concentration, e.g. ppm, normality, % weight for weight, % weight for volume
Different ways of expressing concentration (e.g. ppm, normality, % weight for weight, weight / weight, mass / mass %, weight for volume, w / v, weight / volume w / w.)
Parts per million by mass (ppm, milligrams per kilogram, 0.0 001%) is about equivalent to a grain of sugar in a cup of tea,
Parts per million, ppm, 1 ppm = 1 mg per litre.
3.7.2 Degrees proof, proof spirit
Proof spirit contains, in Britain 49.28% alcohol (ethanol) by weight, 57.10% by volume, relative density 0.920 at 10.6oC (formerly specific gravity of 12 / 13 at 51oF) in USA 50% by volume at 15.6oC. This standard is quoted as 100 degrees of proof, 100o. If a spirituous liquor is p% overproof (above standard strength) it contains as much alcohol in 100 vol as in 100 + p vol of proof spirit. 20o proof = 0.2 X 57.1% alcohol = 11.42% ALC / VOL, e.g. white wine. Concentration of alcohol can also be measured with a hydrometer. Formerly proof spirit was that which if poured over gunpowder and ignited would ignite the gunpowder. If the gunpowder did not ignite, the spirit was under proof.
3.9.0 CGS units (centimetre, gram, second)
Quantity CGS Unit Size
length centimetre 1 cm = 10-2 m
mass gram 1 g = 10-3 kg
area cm2 1 cm2 = 10-4 m2
volume cm3 1 cm3 = 10-6 m3
density g cm-3 1 g cm-3 = 10-3 kg m-3
3.10.0 The m.k.s. units
The metric system of units based on metre, kilogram, second. Also, the electrical unit was the ampere and magnetic constant was 4 pi X 10-7 Hm-1 (henry = H, now SI unit of inductance).
3.11.0 Imperial units used in land surveying (1 hectare = 10,000 m2, 1 km = 1,000 m)
Imperial Metric Imperial Metric
1 square mile 2 58 9 988 ha 1 link 0.201 168 m (exact)
1 square mile 2.589 988 km2 1 foot 0.3 048 m (exact)
1 acre 4 046.856 m2 1 mile 1.609 344 m (exact)
2.471054 acres 1 ha 1 perch 25.2 929 m2
1 rood 1 011.714 m2 0.03 954 perches 1 m2
1 ha = 2.471 acre = 107 639 ft2
1 yard = 0.9 144 metre
1 acre = 0.404 686 hectare
1 square foot = 0.92 903 square metre
3.12.0 SI, CGS and FPS conversion, metric conversion
CGS = centimetre, gram, second
FPS = foot, pound, second
MKS or MKSA = metre, kilogram, second (ampere)
Physical quantity CGS unit FPS unit
length (m = metre) centimetre, 1 cm = 10-2 m foot, 1 ft = 0.3 047 075 m
" . inch, 1 in = 2.54 X 10-2 m
" . mile, 1 mile = 1.61 km
mass (kg = kilogram) gram, 1 g = 10-3 kg pound, 1 lb = 0.45 359 237 kg
" . ounce, 1 oz = 2.835 X 10-2 kg
" . ton, 1 ton = 1.016 X 103 kg
volume 1 cm3 = 10-6 m3 1 ft3 = 2.832 X 10-2 m2
" 1 litre, L =10-3 m3 1 in3 = 1.639 X 10-5 m2
" 1 millilitre, 1 mL = 1 cm3 .
density 1 g cm-3 = 10-3 kg m-3 .
velocity or speed 1 cm s-1 = 10-2 m s-1 .
" 100 km / hour 62.5 miles / hour
force dyne, 1 dyne = 10-5 N .
pressure, stress 1 dyne cm2 = 10-1 Pa .
" bar, 1 bar = 105 Pa 1 bar = 750.07 mm Hg
" millibar = 100 Pa .
energy, work (J = joule) erg, 1 erg = 10-7 J .
power (W = watt) 1 erg S-1 = 10-7 W horsepower, 1 hp = 745.7 W
viscosity poise, 1 P = 10-1 NM-2s .
thermal energy calorie, 1 cal = 4.17 J British thermal unit, 1 BTU = 1.055 X 103 J
3.13.0 Energy conversion KJ, MJ, KWh, therm, BTU, calorie, horsepower
1 KJ = 0.948 BTU
1 MJ = 948 BTU = 0.28 KWh = 0.37 horsepower hours
1 J = 0.239 calories
1 therm = 100 000 BTU = 106 MJ
1 KWh = 3 412 BTU = 3.6 MJ
1 calorie = 4.187 J
1 horsepower = 746 watts
1 horsepower hour = 2.69 MJ
3.13.1 Einstein was right, e = mc2
Albert Einstein's celebrated formula e = mc2 has finally been corroborated, thanks to a mighty computational effort by French, German and Hungarian physicists. A brainpower consortium led b Laurent Lellouch, of France's Centre for Theoretical Physics, using some of the world's most powerful supercomputers, has set down the calculations for estimating the mass of protons and neutrons, the particles at the nucleus of atoms. According to the conventional model of particle physics, protons and neutrons comprise smaller particles known as quarks, which are bound by gluons. The odd thing is the mass of gluons is zero and the mass of quarks is 5 per cent. Where is the missing 95 per cent? The answer, according to the study published in US journal Science, comes from the energy from the movements and interactions of quarks and gluons. In other words, energy and mass are equivalent, as Einstein proposed in his Special Theory of Relativity in 1905. The e = mc2 formula shows that mass can be converted into energy, and energy can be converted into mass. By showing how much energy would be released if a certain amount of mass were to be converted into energy, the equation has been used many times, most famously as the basis for atomic weapons. Resolving e = mc2 at the scale of sub-atomic particles to in equations called quantum chromodynamics to has been fiendishly difficult. “Until now, this has been a hypothesis,” France's National Centre for Scientific Research said proudly in a statement. “It has now been corroborated for the first time." For those keen for more, the computations involve “envisioning space and time as part of a four-dimensional crystal lattice, with discrete points spaced along columns and rows".
AAP (Australian Associated Press) The Australian (newspaper) November 22-23, 2008
3.13.1.1 Quark
The name of the fundamental building block of matter, the quark, comes from the novel "Finnergans Wake" by James Joyce was given this name by Murray Gell-Mann. It is generally pronounced "qwork" to rhyme with "pork".
6.2.0 Different measurements
Traditional counting units, a score, a dozen, common units, market units
Units and scale divisions, analogue units, digital units
6.3.1 SI, The 7 base units: Length, Mass, Time, Electric current, Temperature, Amount of substance, Luminous intensity
The of measurement that form the basis of any system of measurement are the defined mechanical units of mass, length and time. Some fundamental systems also include a unit of electricity. Coordinate systems are used to define the position of a point on a plane using two co-ordinates or in space using three co-ordinates, e.g. Cartesian coordinate system.
Quantity Dimension Name of SI unit Symbol
1. Length
 L metre m
2. Mass M kilogram kg
3. Time T second s
4. Electric current I ampere A
5. Temperature

. kelvin K
6. Amount of substance . mole mol
7. Luminous intensity J candela cd
6.3.1.1 Length, metre
A metre is the length of a path travelled by light in a vacuum during a time interval of 1 / 299 792 458 of a second. Length (l) the kilometre (km), metre (metre)
6.3.1.2 Mass, kilogram
The gram was intended to be the mass of a cubic centimetre of pure water at 4oC. Later, it was defined as one-thousanth part of a kilogram.
A kilogram is the mass of the international prototype kilogram kept in Sevres, France. Proposed alternative definition: A kilogram is such that the Planck constant is exactly 6.6 260 693 X 10-34 joule seconds. Weight: 1000 grams (g) = 1 kilogram (kg), 1000 kg = 1 metric tonne (t)
6.3.1.3 Time, second
A second is the time equal to the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
6.3.1.4 Electric current, ampere
An ampere is the current which, if maintained in two parallel straight conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in a vacuum, would produce between these conductors a force equal to 2 X 10-7 newtons per metre of length. Proposed alternative definition: The ampere is such that the elementary charge is exactly 1.60 217 653 X 10-19 coulombs. (1 coulomb = 1 ampere second)
6.3.1.5 Temperature, Fahrenheit scale, Celsius scale, Kelvin scale
See diagram 7.6: Celsius temperature scale
The temperature of a body is its hotness or coldness with reference to a standard of comparison. Temperature varies with the amount of heat energy in the body.
1. The Fahrenheit temperature scale (Gabriel Fahrenheit 1686 - 1736) has graduations on the thermometer based on a lower fixed point of 32oF, the freezing point of water, and an upper fixed point of 212oF, the boiling point of water. So the fundamental interval is 180 Fahrenheit degrees, 180oF. The Fahrenheit scale is still used in USA.
2. The Celsius temperature scale (Anders Celsius 1701 -1744) has graduations on the thermometer based on a lower fixed point of 0oC, the freezing point of water, and an upper fixed point of 100oC, the boiling point of water. So the fundamental interval is 100 Celsius degrees. The Celsius scale was formerly called the centigrade scale, "100 steps" scale, Some people still incorrectly quote temperatures in "degrees centigrade". C = "Celsius" NOT "Centigrade".
To convert the Fahrenheit scale to the Celsius scale (F-32) / 9 = C/5. The Celsius and Fahrenheit scales have the same value at -40oC or -40oF. Human body temperature = 37oC (Celsius) or 98.6oF (Fahrenheit)
3. The Kelvin scale (Lord Kelvin 1824 - 1907) is based on the idea of absolute zero. Molecular motion, heat, approaches zero as the temperature approaches -273.15oC. One kelvin degree, 1 K = 1 Celsius degree, 1oC. Absolute zero = -273.15oC = 0K, not "degree Kelvin". To convert the Celsius scale to the Kelvin scale, add 273.15. For example, 0oC = 273.15 K, 100oC = 373.15 K, and 10oC = 283.15 K. So this scale begins at absolute zero and increases in kelvins. The Kelvin scale is the preferred scale for scientific experiments.
The temperature, kelvin, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
Proposed alternative definition of temperature, kelvin: The kelvin is such that the Boltzmann constant is exactly 1.3806505 X 10-23 joules per kelvin.
Equivalent temperatures in different scales
.
 Kelvin Celsius Fahrenheit
Absolute zero 0oK -273oC -459oF
Freezing point of water 273oK 0oC 32oF
Boiling point of water 373oK 100oC 212oF
6.3.1.5.1 Triple point and ice point temperatures of water
See diagram 7.8: Triple point of water
The triple point is the temperature at which the three phases of a substance can exist together. The triple point temperature of water is the equilibrium point = 0.01°C (273.16 K) and 611.2 Pa (N m-2) in a sealed vacuum flask. It is an important fixed point for kelvin and thermodynamic scales of temperature.
The ice point temperature, 273.15 K, is the temperature when equilibrium exists between ice and water at standard pressure. It is the lower fixed point of the Celsius scale.
6.3.1.7 Luminous intensity, candela, cp
A candela is the intensity in a given direction, of a light source that emits monochromatic radiation of frequency 540 X 1012 hertz with a radiant intensity in that direction of 1 / 683 watts per steradian.
The previous unit was the candlepower, about 0.98 of a candela, that was defined in various ways, including the light from a standard whale oil candle. However, people liked to continue to use the term candlepower, so nowadays 1 candlepower = 1 candela. The zirconium wire in a camera flash cube ignites to release a 2 000 modern candlepower burst of light for about 30 millionths of a second.
6.3.3 SI derived units
These units are physical quantities formed from the base units. Some of these units are as follows:
Quantity Dimension Unit name Symbol Equivalent
1. Velocity (speed) L T-1 . v
 m s-1
2. Acceleration L T-2 . a
 m s-2
3. Momentum M L T-1 . Mv
 kg m s-1
4. Force M L T-2 newton N kg m s-2 = J m-1
5. Pressure (stress) M L-1T-2 pascal Pa N m-2
6. Energy (work) M L2T-2 joule J N m
7. Power M L2 T-3 watt W J s-1
8. Electric charge . coulomb C A s
9. Electric potential difference . volt V W A-1
10. Electric capacitance . farad F C V-1
11. Electric resistance . ohm omega V A-1
12. Frequency T-1 hertz Hz s-1
13. Radioactivity T-1 becquerel Bq s-1
14. Viscosity M L-1T-1 poise P 1 P = 0.1 NM-2s
15. Density M L-3 . kg m-3 .
16. Plane angle . radian rad = 180o / pi
6.3.3.1 Other derived units based on SI
Physical quantity Name of unit Symbol
Surface tension newton per metre N m-1
Electric field strength volt per metre V m-1
Magnetic field strength ampere per metre A m-1
Specific heat capacity joule per kilogram kelvin J kg-1 K-1
Concentration mole per cubic metre mol m-3
6.3.3.2 Angle, degree, arc minute, arc second, radian
Angle is the measurement of the inclination of one line to another. Measured in degrees, such that 360 degrees (360o) = 1 revolution. Also, measured in radians, such that 2 pi radians = 1 revolution. The degree can be divided into arc minutes, arcmin, such that 1' = 1/60 of a degree, and divided into arc seconds, arcsec, such that 1" = 1 / 3 600 of a degree. Arc minutes and arc seconds are used in astronomy to measure the diameter or separation of astronomical objects.
6.3.3.5 Units used with SI units
Physical quantity Name of unit Symbol Definition of unit
Area hectare ha 104 m2
Mass tonne t 103 kg = Mg
Pressure bar bar 105 N m-2
Volume litre l 10-3 m3 = dm3
6.3.5 SI prefixes
Decimal fractions and multiples
Symbol........................................Prefix...........................................Factor X
T tera, X 1000,000,000,000 1012
G giga, X 1000,000,000 109
M mega, X 1000,000 106
k kilo, X 1000 103
h hecto, X 100 102
da deca, X 10 10
d deci, X 0.1 10-1
c centi, X 0.01 10-2
m milli, X 0.001 10-3
mu micro, X 0.000001 10-6
n nano, X 0.000000001 10-9
p pico, X 0.000000000001 10-12
6.3.6 SI, CGS and FPS conversion, metric conversion
CGS = centimetre, gram, second
FPS = foot, pound, second
MKS or MKSA = metre, kilogram, second, (ampere)@@@
Physical quantity CGS unit FPS unit
length (m = metre) centimetre, 1 cm = 10-2 m foot, 1 ft = 0.3048 m
" . inch, 1 in = 2.54 X 10-2 m
" . mile, 1 mile = 1.61 km
mass (kg = kilogram) gram, 1 g = 10-3 kg pound, 1 lb = 0.4536 kg
" . ounce, 1 oz = 2.835 X 10-2 kg
" . ton, 1 ton = 1.016 X 103 kg
volume 1 cm3 = 10-6 m3 1 ft3 = 2.832 X 10-2 m2
" 1 litre, L =10-3 m3 1 in3 = 1.639 X 10-5 m2
" 1 millilitre, 1 mL = 1 cm3 .
density 1 g cm-3 = 10-3 kg m-3 .
velocity or speed 1 cm s-1 = 10-2 m s-1 .
" 100 km / hour 62.5 miles / hour
force dyne, 1 dyne = 10-5 N .
pressure, stress 1 dyne cm2 = 10-1 Pa .
" bar, 1 bar = 105 Pa 1 bar = 750.07 mm Hg
" millibar = 100 Pa .
energy, work (J = joule) erg, 1 erg = 10-7 J .
power (W = watt) 1 erg S-1 = 10-7 W horsepower, 1 hp = 745.7 W
viscosity poise, 1 P = 10-1 NM-2s .
thermal energy calorie, 1 cal = 4.17 J British thermal unit, 1 BTU = 1.055 X 103 J
6.4.0 Errors, theory of errors, addition of uncertainties
Accuracy and precision, possible error, least count
Errors by 10 students, standard error
Measurement errors, parallax error, zero error \ index error and correction, systematic error
Random errors and system errors, scale error, probable error
Significant figures - all the figures that can be read with meaning from an instrument
Standard form (scientific notation), e.g. 8.04 X 102 shows the significant figures expressed unambiguously
The reading below, as shown by the arrow, is 98.5. The 9 and the 8 are certain figures. The 5 is uncertain. The absolute error is half the smallest division of the scale being read, i.e. 0.5. So the reading in absolute error form is: 98 + or - 0.5.
.. 100
.. 99
->
.. 98
.. 97
6.12.0 Weights of one matchbox full of fertilizer
Ammonium sulfate (sulfate of ammonia) 26 g
Potassium sulfate (sulfate of potash) 40 g
Potassium chloride (muriate of potash) 24 g
Single superphosphate, "super" 22 g
Triple superphosphate, "super" 20 g
Sulfur 20 gm
6.13.0 Roman numerals
I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000
6.14.0 Oven temperatures
oC oF Gas mark Description
110 225 1/4 very cool, very slow
120 250 1/2 .
140 275 1 cool
150 300 2 .
170 325 3 very moderate
180 350 4 moderate
190 375 5 .
200 400 6 moderately hot
220 425 7 hot
230 450 8 .
240 475 9 very hot